BACKGROUND:These creatures are huge blocks of stone brought to life by the black
magic of the Koopa Troop. They're usually blue, and usually have pointy
rock "spines" sticking out all around them.
Bowser first had these creatures brought to life around the time he attempted
to take over the Mushroom World by having his Koopalings steal the magic wands from the Seven Kings. He meant to use them as "smart" traps in his fortresses. The incantation cast by his team of Magikoopas was so powerful, though, that it reached out beyond the intended area, and enchanted some stones that were unintended. This resulted in the creation of a few wild
Thwomps which can usually be found in mountains or caves. However, most Thwomps are tame, and can only be found in Koopa territory.
All Thwomps, be they wild or tame, follow a similar pattern: They hover in the air, watching for someone to pass by, then THWOMP! They attempt
to crush them. They don't pay any attention to what's going on below them when they're moving up, so sneak by them then.
It's interesting to note that Thwomps seem to be getting dumber. They
used to wait for someone to come nearby before attacking, but many now
just attack in a regular pattern. Some observers think thtat the spell
Bowser had cast on them is wearing off.

EVOLUTION:Thwomps first appeared in Super Mario Bros.3, and except for their eyes, they looks surprisingly close to the drawings (see the drawing
above - it comes from the SMB3 manual)
In Super Mario World, Thwomps changed colour to grey. Like many creatures
that changed at the time, it is assumed that this was a one-generation
mutation, although that is questionable, since Thwomps don't breed.
Another theory is that Bowser had a new batch of Thwomps made in
Dinosaur Land, and the different properties of the stone there caused
the unusual colouring.
In Super Mario RPG, they returned to their original look, and they
were done quite nicely, I must add. Many of the characters in that game
feel overly geometric to mee, but Thwomps came out very well, probably
partially because they're more or less block-shaped to start with.
Super Mario 64 brought them back, but they were a bit funny looking,
because all the spikes had been removed from them. It is possible that
this is another new batch made by Bowser after he entered the painting
worlds of that game. (Actually, the truth is, they probably didn't have
enough polygons, but that's another story...)